Recently it has been argued that, because tachyonic matter satisfies the Strong Energy Condition [SEC], there is little hope of avoiding the singularities which plague S-Brane spacetimes. Meanwhile, however, Townsend and Wohlfarth have suggested an ingenious way of circumventing the SEC in such situations, and other suggestions for actually violating it in the S-Brane context have recently been...

We study the so-called “Smith is Huq” condition in the context of Sprotomodular categories: two S-equivalence relations centralise each other if and only if their normalisations commute. We prove that this condition is satisfied by every category of monoids with operations equipped with the class S of Schreier split epimorphisms. Some consequences in terms of characterisation of internal struct...

The papers [5], [12], [3], [1], [6], [2], [10], [9], [4], [11], and [7] provide the notation and terminology for this paper. We introduce BCI stuctures with complements which are extensions of BCI structure with 0 and zero structure and are systems 〈 a carrier, an external complement, an internal complement, a zero 〉, where the carrier is a set, the external complement and the internal compleme...

Permutations over F22k with low differential uniform, high algebraic degree and high nonlinearity are of great cryptographical importance since they can be chosen as the substitution boxes (S-boxes) for many block ciphers. A well known example is that the Advanced Encryption Standard (AES) chooses a differentially 4-uniform permutation, the multiplicative inverse function, as its S-box. In this...